Box dimension of interpolations of self-similar processes with stationary increments

• Autorzy: Herburt I.
• Języki publikacji: EN

Abstrakty

EN

We prove that under a general condition interpolation dimensions of H-sssi process converge in probability to 2−H.The result can be applied to a wideclass of H-sssi processes which includes fractional Brownian motions, (α, β)-fractional stable processes or strictly stable H-sssi processes. Moreover, we prove that for an H-sssi process with continuous sample paths the same general condition implies uniform convergence in probability of sample paths o f fractal interpolations to sample paths of the interpolated process.

Słowa kluczowe

EN

fractal interpolation; interpolation dimension; box dimension; self-similar process; stationary increments; stable process

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2001
• Tom: Vol. 21, Fasc. 1
• Strony: 171--178
• Opis fizyczny: Biblogr. 7 poz.

Twórcy

autor

Herburt I.

• Warsaw University of Technology Warsaw, Poland

Bibliografia

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• [4] A. N. Shiryayev, Probability, Springer, 1984.
• [5] K. Takashima, Sample paths properties of ergodic self-similar processes, Osaka J. Math. 26 (1989), pp. 159-189.
• [6] W. Vervaat, Sample paths properties of self-similar processes with stationary increments, Ann. Probab. 13 (1985), pp. 1-27.
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